Translation:A strong wind blows.
Noisy-cricket, maybe that's a British English thing, but as an American, "There is a wind blowing outside" is something I'd only expect to hear from a foreigner with broken English. To get that particular point across, I'd say "The wind is blowing outside" or "It's windy outside."
As for the phrase "a wind," the only time I can imagine it being used is if someone's trying to be poetic, and goes on to describe the wind in detail. But it would be blatantly obvious that they're doing it on purpose. Most of the time you'd say "a gust of wind" instead, unless maybe you're describing a specific instance where the wind suddenly became strong, as in "We finally finished setting the picnic table, and then a strong wind came and blew the tablecloth right off the table."
That being said, strong is the only adjective I can think of that works like that. If you're using other words to describe a particular instance of wind, like hot, freezing, big, small, etc., you'd say, for example, "A hot gust of wind." "A hot wind" just sounds weird.
As an American-English speaker myself, I kind of disagree. Talking about "a wind" is uncommon, but not unusual. The wording brings to mind one specific kind of wind (i.e., "the north wind") so saying "a wind blows outside" is like saying "one of the winds is outside right now" without specifying which one, but recognizing that it's one of them. Granted, most natural examples coming to mind involve sailing, or some other activity in which the wind is a major factor/where multiple "winds" are present. "A north wind caught the sail," for instance.
When you say "strong winds will blow", you're making a prediction. You shouldn't use the regular form of the verb to convey a prediction, so in this case 吹きます (fukimasu) is best translated in the present tense. If you want to make a prediction about the weather, you use でしょう (deshou).
Tsuyoi kaze ga fuku deshou.
Strong winds will blow.
I wrote "There is a strong wind blowing." I was told i was wrong and that the correct answer is "a strong wind blows." You could make the case for complex tense (ふいています）but we very rarely use the inifinitive in a sentence in english so i would imagine mine should be a valid translation.